Deforming the initial cube by mouse
I don't have a tool that does this for you, but you can manipulate the shape yourself. Here's how I would do it:

go to edit mode (either press Tab or go to the left corner, change it from Object Mode to Edit mode) you know that you are in Edit Mode if you see the vertices of the cube as dots

now select 4 vertices while holding Shift (the selected vertices appear orange and the one you selected last is white)

press S (for changing the scale) and then press Y (to scale it along the Y-axis, but you could also press X to scale it along the X-axis or Z)

to scale it you just need to move your mouse in the direction you want to scale it
if you are still in the scaling mode (you see a dotted black line coming from the center of your object), you can switch between the axes by pressing X, Y or Z and continue scaling along them

Hope this helps
(if you just want to move one vertex at a time, just click on the one you want to move and then press G to move it in space or G and then Z to move it along the Z-axis)